The full design matrix allows for a quadratic surface response function between the hydrological response function and the receptor impact variables. This includes linear terms, pairwise interactions between the linear terms and quadratic terms for all hydrological response variables. If the hydrological response variables vary in the reference period, then an interaction between the quadratic surface response function and the future period is also included. The full design model structures the elicitation scenario so that this complex model can be elucidated.
However, the full richness of the model may be excessive for simple relationships between hydrological response variables and receptor impact variables. Simpler models are therefore considered. Optional model terms include: interactions between hydrological response variables and the future period, the pairwise interactions between different hydrological response variables and the quadratic terms. The alternative models are ranked using a Bayesian information criterion (BIC) (proportional to the Schwarz criterion; Schwarz, 1978) metric:
|
|
(37) |
where 
is the dimension of the vector 
and 
. The model with the lowest BIC value is selected as the best model.
Note that several terms are required to be retained within all the candidate models. These include: the intercept, the future-period factor, the short-term factor, the influence of 
and at least the linear terms of all hydrological response variables to be considered in the receptor impact modelling elicitation workshop. The inclusion of this minimal subset ensures that the covariates which provide the structure for the elicitation scenarios are also represented in the estimation and prediction steps of the receptor impact modelling.